{"id":"https://openalex.org/W4382193144","doi":"https://doi.org/10.3390/sym15051041","title":"A Mathematical Theoretical Study of a Coupled Fully Hybrid (k, \u03a6)-Fractional Order System of BVPs in Generalized Banach Spaces","display_name":"A Mathematical Theoretical Study of a Coupled Fully Hybrid (k, \u03a6)-Fractional Order System of BVPs in Generalized Banach Spaces","publication_year":2023,"publication_date":"2023-05-08","ids":{"openalex":"https://openalex.org/W4382193144","doi":"https://doi.org/10.3390/sym15051041"},"language":"en","primary_location":{"id":"doi:10.3390/sym15051041","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15051041","pdf_url":"https://www.mdpi.com/2073-8994/15/5/1041/pdf?version=1683595942","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/5/1041/pdf?version=1683595942","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089988235","display_name":"Abdelatif Boutiara","orcid":"https://orcid.org/0000-0002-6032-4694"},"institutions":[{"id":"https://openalex.org/I4210115782","display_name":"University of Ghardaia","ror":"https://ror.org/02ck5yd04","country_code":"DZ","type":"education","lineage":["https://openalex.org/I4210115782"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Abdellatif Boutiara","raw_affiliation_strings":["Laboratory of Mathematics and Applied Sciences, University of Ghardaia, Ghardaia 47000, Algeria"],"affiliations":[{"raw_affiliation_string":"Laboratory of Mathematics and Applied Sciences, University of Ghardaia, Ghardaia 47000, Algeria","institution_ids":["https://openalex.org/I4210115782"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078232638","display_name":"Sina Etemad","orcid":"https://orcid.org/0000-0002-1574-1800"},"institutions":[{"id":"https://openalex.org/I51301133","display_name":"Azarbaijan Shahid Madani University","ror":"https://ror.org/05pg2cw06","country_code":"IR","type":"education","lineage":["https://openalex.org/I51301133"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Sina Etemad","raw_affiliation_strings":["Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran","institution_ids":["https://openalex.org/I51301133"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023573264","display_name":"Sabri T. M. Thabet","orcid":"https://orcid.org/0000-0002-4568-9732"},"institutions":[{"id":"https://openalex.org/I70374766","display_name":"University of Aden","ror":"https://ror.org/02w043707","country_code":"YE","type":"education","lineage":["https://openalex.org/I70374766"]}],"countries":["YE"],"is_corresponding":false,"raw_author_name":"Sabri T. M. Thabet","raw_affiliation_strings":["Department of Mathematics, University of Aden, Aden 124, Yemen","Department of Mathematics, University of Lahej, Lahej 73560, Yemen"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Aden, Aden 124, Yemen","institution_ids":["https://openalex.org/I70374766"]},{"raw_affiliation_string":"Department of Mathematics, University of Lahej, Lahej 73560, Yemen","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086599287","display_name":"Sotiris K. Ntouyas","orcid":"https://orcid.org/0000-0002-7695-2118"},"institutions":[{"id":"https://openalex.org/I194019607","display_name":"University of Ioannina","ror":"https://ror.org/01qg3j183","country_code":"GR","type":"education","lineage":["https://openalex.org/I194019607"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Sotiris K. Ntouyas","raw_affiliation_strings":["Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece","institution_ids":["https://openalex.org/I194019607"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053506086","display_name":"Shahram Rezapour","orcid":"https://orcid.org/0000-0003-3463-2607"},"institutions":[{"id":"https://openalex.org/I4210126829","display_name":"China Medical University Hospital","ror":"https://ror.org/0368s4g32","country_code":"TW","type":"healthcare","lineage":["https://openalex.org/I4210126829"]},{"id":"https://openalex.org/I184693016","display_name":"China Medical University","ror":"https://ror.org/00v408z34","country_code":"TW","type":"education","lineage":["https://openalex.org/I184693016"]},{"id":"https://openalex.org/I51301133","display_name":"Azarbaijan Shahid Madani University","ror":"https://ror.org/05pg2cw06","country_code":"IR","type":"education","lineage":["https://openalex.org/I51301133"]}],"countries":["IR","TW"],"is_corresponding":true,"raw_author_name":"Shahram Rezapour","raw_affiliation_strings":["Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran","Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran","institution_ids":["https://openalex.org/I51301133"]},{"raw_affiliation_string":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan","institution_ids":["https://openalex.org/I4210126829","https://openalex.org/I184693016"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051443783","display_name":"Jessada Tariboon","orcid":"https://orcid.org/0000-0001-8185-3539"},"institutions":[{"id":"https://openalex.org/I82828225","display_name":"King Mongkut's University of Technology North Bangkok","ror":"https://ror.org/04fy6jb97","country_code":"TH","type":"education","lineage":["https://openalex.org/I82828225"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Jessada Tariboon","raw_affiliation_strings":["Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand","Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand"],"affiliations":[{"raw_affiliation_string":"Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand","institution_ids":["https://openalex.org/I82828225"]},{"raw_affiliation_string":"Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand","institution_ids":["https://openalex.org/I82828225"]}]}],"institutions":[],"countries_distinct_count":6,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5051443783","https://openalex.org/A5053506086"],"corresponding_institution_ids":["https://openalex.org/I184693016","https://openalex.org/I4210126829","https://openalex.org/I51301133","https://openalex.org/I82828225"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":5.5522,"has_fulltext":true,"cited_by_count":25,"citation_normalized_percentile":{"value":0.96730999,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"15","issue":"5","first_page":"1041","last_page":"1041"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.994700014591217,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7717369794845581},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.747635006904602},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.7077028751373291},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.6152025461196899},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5130075812339783},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4897153675556183},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.47816330194473267},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.47710567712783813},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.42589038610458374},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.42021873593330383},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4116445481777191},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39764806628227234},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12311485409736633}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7717369794845581},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.747635006904602},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.7077028751373291},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.6152025461196899},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5130075812339783},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4897153675556183},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.47816330194473267},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.47710567712783813},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.42589038610458374},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42021873593330383},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4116445481777191},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39764806628227234},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12311485409736633},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15051041","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15051041","pdf_url":"https://www.mdpi.com/2073-8994/15/5/1041/pdf?version=1683595942","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:77520464b4f843b182e810c1bde5c3f2","is_oa":true,"landing_page_url":"https://doaj.org/article/77520464b4f843b182e810c1bde5c3f2","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 5, p 1041 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/5/1041/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15051041","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15051041","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15051041","pdf_url":"https://www.mdpi.com/2073-8994/15/5/1041/pdf?version=1683595942","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5590106218","display_name":null,"funder_award_id":"KMUTNB-FF-66-11","funder_id":"https://openalex.org/F4320324344","funder_display_name":"King Mongkut's University of Technology North Bangkok"}],"funders":[{"id":"https://openalex.org/F4320322530","display_name":"Azarbaijan Shahid Madani University","ror":"https://ror.org/05pg2cw06"},{"id":"https://openalex.org/F4320324344","display_name":"King Mongkut's University of Technology North Bangkok","ror":"https://ror.org/04fy6jb97"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4382193144.pdf","grobid_xml":"https://content.openalex.org/works/W4382193144.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W1987168297","https://openalex.org/W2060220674","https://openalex.org/W2291466341","https://openalex.org/W2488882192","https://openalex.org/W2520410115","https://openalex.org/W2556784265","https://openalex.org/W2728168734","https://openalex.org/W2898923932","https://openalex.org/W2963641381","https://openalex.org/W2999642714","https://openalex.org/W3035235874","https://openalex.org/W3035594241","https://openalex.org/W3049243963","https://openalex.org/W3092318040","https://openalex.org/W3097301788","https://openalex.org/W3133739991","https://openalex.org/W3143946795","https://openalex.org/W3153189436","https://openalex.org/W3164198489","https://openalex.org/W3170394055","https://openalex.org/W3171099174","https://openalex.org/W3207439583","https://openalex.org/W4200492170","https://openalex.org/W4214871329","https://openalex.org/W4285390719","https://openalex.org/W4296946189","https://openalex.org/W4301223505","https://openalex.org/W4304471500","https://openalex.org/W4306742557","https://openalex.org/W4313344976","https://openalex.org/W4313898161","https://openalex.org/W4318043099","https://openalex.org/W4320918846","https://openalex.org/W6730176618","https://openalex.org/W6740529608","https://openalex.org/W6784338275","https://openalex.org/W6796506016","https://openalex.org/W6839943104"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W4301247218","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W2129818458","https://openalex.org/W4289551052","https://openalex.org/W2340777379","https://openalex.org/W4390756076","https://openalex.org/W4243074410"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,29],"study":[4],"a":[5,44],"coupled":[6],"fully":[7],"hybrid":[8],"system":[9],"of":[10,43,54,74],"(k,\u03a6)\u2013Hilfer":[11],"fractional":[12],"differential":[13],"equations":[14],"equipped":[15],"with":[16,37],"non-symmetric":[17],"(k,\u03a6)\u2013Riemann-Liouville":[18],"(RL)":[19],"integral":[20],"conditions.":[21],"To":[22],"prove":[23],"the":[24,31,41,50,55,61,72],"existence":[25],"and":[26,33],"uniqueness":[27],"results,":[28],"use":[30],"Krasnoselskii":[32],"Perov":[34],"fixed-point":[35],"theorems":[36],"Lipschitzian":[38],"matrix":[39],"in":[40],"context":[42],"generalized":[45],"Banach":[46],"space":[47],"(GBS).":[48],"Moreover,":[49],"Ulam\u2013Hyers":[51],"(UH)":[52],"stability":[53],"solutions":[56],"is":[57,68],"discussed":[58],"by":[59],"using":[60],"Urs\u2019s":[62],"method.":[63],"Finally,":[64],"an":[65],"illustrated":[66],"example":[67],"given":[69],"to":[70],"confirm":[71],"validity":[73],"our":[75],"results.":[76]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":3}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}